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PHYSICS AND TECHNOLOGY SYSTEM OF UNITS FOR ELECTRODYNAMICS∗ M. G. Ivanov† Moscow Institute of Physics and Technology Dolgoprudny, Russia Abstract The contemporary practice is to favor the use of the SI units for electric circuits and the Gaussian CGS system for electromagnetic field. A modification of the Gaussian system of units (the Physics and Technology System) is suggested. In the Physics and Technology System the units of measurement for electrical circuits coincide with SI units, and the equations for the electromagnetic field are almost the same form as in the Gaussian system. The XXIV CGMP (2011) Resolution ¾On the possible future revision of the International System of Units, the SI¿ provides a chance to initiate gradual introduction of the Physics and Technology System as a new modification of the SI. Keywords: SI, International System of Units, electrodynamics, Physics and Technology System of units, special relativity. 1. Introduction. One and a half century dispute The problem of choice of units for electrodynamics dates back to the time of M. Faraday (1822–1831) and J. Maxwell (1861–1873). Electrodynamics acquired its final form only after geometrization of special relativity by H. Minkowski (1907–1909). The improvement of contemporary (4-dimentional relativistic covariant) formulation of electrodynamics and its implementation in practice of higher education stretched not less than a half of century. Overview of some systems of units, which are used in electrodynamics could be found, for example, in books [2, 3] and paper [4]. Legislation and standards of many countries recommend to use in science and education The International System of Units (SI). Electrodynamical units of SI originates from the practical system of units, which was established at The First International Congress of Electricians (Paris, 1881). Units of practical system are multiples of CGSM units (the CGSM is one of old and now obsolete version of the CGS system of units), which were too small for practical applications. Nevertheless, the using of the SI in electrodynamics is still a matter of objections. The Gaussian (symmet- rical) CGS-system (CGS) is very popular among physicists. The CGS is more consistent with symmetries of electrodynamics. The CGS is a standard for scientific publications and textbooks on theoretical physics. One could (with some exaggerating) declare that the SI is system for measurements and the CGS is system for formulae and analytical calculations. arXiv:1512.05394v2 [physics.class-ph] 30 Dec 2015 Today the standard for electrical circuits is the SI, but for electromagnetic field the standard is the CGS. E.g. the CGS is used in classical textbook by I.Ye. Tamm “Basic theory of electricity” [5], but the practical units (the predecessors of electrical units of the SI) are used for the alternating current (§ 80 of [5]). The similar preferences are common not only for the classics of science, but for today students and professors in Moscow Institute of Physics and Technology. The problem of choice of units for electrodynamics is still actual, moreover, it becomes more actual. The International Bureau of Weights and Measures in the last 8-th edition of its official brochure “The International System of Units (SI)” [6] admits (“Units outside the SI”, the 2-nd paragraph, some word are highlighted by italic font by M.I.) ∗The paper is extended version of the paper [1], published in Russian. †Mikhail G. Ivanov. e-mail: [email protected] 1 Individual scientists should also have the freedom to sometimes use non-SI units for which they see a particular scientific advantage in their work. An example of this is the use of CGS-Gaussian units in electromagnetic theory applied to quantum electrodynamics and relativity. Reading this text one has to remember, that coherent modern representation of the electrodynamics without special relativity is impossible. It is clear, that the main message of this disclaimer applies primarily to usage of the CGS system. The previous 7-th edition of the brochure “The International System of Units (SI)” [7] does not contain this disclaimer. The softer attitude towards the CGS system is probably associated with the planned change of definition of kilogram, ampere, mole and kelvin in the SI by fixing exact numerical values of the Plank constant, the elementary charge, the Avogadro constant and the Boltzmann constant [8]. This redefinition requires new exact measurements and calculations, which use methods of quantum electrodynamics. Just in quantum electrody- namics the CGS looks preferable in comparison with the SI for many physicists. 2. Criticism of the SI Usage of the SI in theoretical research is complicated. The SI-units of electrodynamic quantities do not consistent with symmetries of the theory, which related with special relativity. This inconsistency is related with different dimensions of the electric and magnetic fields E and H and the inductions D and B. It makes difficult usage of the SI in the teaching of electrodynamics, especially in the cases where a student has to have a solid understanding of the theory structure. Because of this reason theoretical physics courses in leading Russian universities traditionally use the CGS. The problem was considered in paper by D.V. Sivukhin “The international system of physical units” [9] (see also [10], where the comparison of the SI and the CGS is presented), published in 1979 in the journal “Soviet Physics Uspekhi” by the decision of the Division of General Physics and Astronomy of the USSR Academy of Sciences. That practically means the unified position of community of Russian physicists. We present a vivid quote from this article: In this respect, the SI system is no more logical than, say, a system in which the length, width, and height of an object are expressed not only in terms of different units but have different dimensions as well. The inconsistence of the SI with the symmetries of electrodynamics due to historical reasons, because the foundations of the system were set before the creation of special relativity. Moreover, the units of volt, ampere, ohm, farad, etc. (ascending to the practical system) are intensively used in technics, are involved in the SI and are not involved in the CGS1. When in 1948 these units were introduced in the SI, role of the special relativity for electrodynamics was still not sufficiently understood by many physicists-experimenters and engineers. You could ever dream of how to change these units in the early XX century, but now this units and related standards are widely used not only in measuring devices, but in the whole technique, including home electronics. This makes it virtually impossible any revision of the SI, which excludes from the system ampere, as the basic unit of. Can we combine the wishes of the engineers and theorists? Yes, we can! 3. What system of units do we need? 3.1. The wishes of a theorist Electric field strength E and induction D have to be of the same dimension, and in the vacuum E = D. • Electric field induction B and strength H have to be of the same dimension, and in the vacuum B = H. • Fields E and B have to be of the same dimension, and in the vacuum for flat traveling wave E = B . • v | | | | Magnetic field of a moving charge is a relativistic effect, so the formula have to contain c . To remove speed • of light by redefinition of units is unnatural. 1In the beginning of XX century in Russia capacitors were fabricated, labeled in the CGS system. The CGS unit of capacitance is the centimeter [11]. 2 v The Lorentz force is a relativistic effect, so the formula have to contain c . To remove speed of light by • redefinition of units is unnatural. 1 Introducing of constant 4π into the Coulomb law (it was suggested by O. Heaviside) is natural, because • it removes the factor 4π (the surface area of two-dimensional unit sphere) in Maxwell equations and in formulae for energy and action of electromagnetic field. It is consistent with the practice of theorists which consider spaces with dimensions other then 3. For the standard electrodynamics this rationalisation makes no bad nor good. 3.2. The wishes of an engineer and an experimenter The SI units for electrical circuits (ampere, volt, ohm, farad, henry) are used everywhere in devices and • standards, they could not be changed. The appearance of the speed of light in equations for electrical circuits is undesirable. • Fields D and H could not be measured directly, so their units are not used in any devices. This units are • not very important. 3.3. How to reconcile theorists with engineers We propose to modify the SI without changing the base units (kilogram, metre, second, ampere, mole, kelvin, candela), but modifying the form of the equations of electrodynamics (to make them similar to equations in the CGS) by changing the constant factors. Due to this change of factors some SI derived units have to be changed. We preserve from old SI (SIold) ampere as unit for current, and all derived units, which do not involve fields D, B and H. So the units of charge coulomb = C, of electric potential volt = V, of electrical resistance ohm =Ω, of capacitance farad = F, of inductance henri = H remain the same. The Coulomb law and the strength of electrical field reman the same form as in SIold 1 q1q2 q1q2 1 q q F = 2 = ke 2 , E = 2 = ke 2 . 4πε0 r r 4πε0 r r 1 1 2 Here ke = 4πε0 is Coulomb constant, q , q , q are electrical charges. We redefine the fields D, H and B according to above “The wishes of a theorist”, all these fields have the V same unit m , just like field E.
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